To solve this problem, we need to identify another angle with the same trigonometric ratio for each given angle. Here’s the detailed explanation for each part:

Step-by-step solution:

1. a) $\cos 45^\circ$:

   • The cosine function is positive in Quadrants I and IV.
   • $\cos 45^\circ = \cos (360^\circ - 45^\circ) = \cos 315^\circ$.
   • Therefore, another angle is $\mathbf{315^\circ}$.

2. b) $\sin 150^\circ$:

   • The sine function is positive in Quadrants I and II.
   • $\sin 150^\circ = \sin (180^\circ - 150^\circ) = \sin 30^\circ$.
   • Therefore, another angle is $\mathbf{30^\circ}$.

3. c) $\tan 300^\circ$:

   • The tangent function is positive in Quadrants I and III.
   • $\tan 300^\circ = \tan (300^\circ - 180^\circ) = \tan 120^\circ$, but tangent is negative there.
   • Using ( \tan (360^\circ - 300^\circ) = }, same